Hamlet (1948) [Ophelia]: Drowned (off-camera) in a river; we see her floating in the water and singing, but the actual drowning occurs after she drifts off-screen. Her body is shown afterwards at her funeral.

Angel Face(1952) [Diane Tremayne]: Killed in a car crash (along with Robert Mitchum) when she drives their car over a cliff. (Thanks to Dick Hertz)

The Robe (1953) [Diana]: Executed (off-screen), along with Richard Burton, by a firing squad of archers; the movie ends as they are walking together to the execution. (Their deaths are confirmed in the 1954 sequel Demetrius and the Gladiators.) (Thanks to Mac)

The Egyptian (1954) [Merit]: Shot in the chest with an arrow. (Thanks to MC)

Elmer Gantry (1960) [Sister Sharon Falconer]: Burned to death after a fire breaks out in her revival tent and she refuses to leave. We see her standing inside the burning tent, followed by an exterior shot as it burns to the ground.